Source Reconstruction Algorithms Research Articles

An equivalent surface dipoles based electric field to magnetic field transformations for estimating radiated emissions

The new generation of communication devices operating in higher frequency bands is constantly pushing the complexity of field measurements for electromagnetic compliance and the design of field probes. These compliance are to be met for both electric and magnetic fields, of which if one set is available, the other can be estimated computationally using source reconstruction algorithms. The main objective of this paper is to refine the dipole-based source reconstruction algorithms using surface equivalence principle. Compared to earlier works, the algorithm is based on a novel way of placing a single dipole per point tangentially to a fictitious surface based on surface equivalence theorem instead of multiple orthogonal dipoles per point. The numerical results are compared with the state-of-art to demonstrate the effectiveness in obtaining accurate fields and locating the regions of the Device Under Test responsible for overshooting the interference limits.

TDCOSMO

The importance of alternative methods for measuring the Hubble constant, such as time-delay cosmography, is highlighted by the recent Hubble tension. It is paramount to thoroughly investigate and rule out systematic biases in all measurement methods before we can accept new physics as the source of this tension. In this study, we perform a check for systematic biases in the lens modelling procedure of time-delay cosmography by comparing independent and blind time-delay predictions of the system WGD 2038−4008 from two teams using two different software programs: GLEE and LENSTRONOMY. The predicted time delays from the two teams incorporate the stellar kinematics of the deflector and the external convergence from line-of-sight structures. The un-blinded time-delay predictions from the two teams agree within 1.2σ, implying that once the time delay is measured the inferred Hubble constant will also be mutually consistent. However, there is a ∼4σ discrepancy between the power-law model slope and external shear, which is a significant discrepancy at the level of lens models before the stellar kinematics and the external convergence are incorporated. We identify the difference in the reconstructed point spread function (PSF) to be the source of this discrepancy. When the same reconstructed PSF was used by both teams, we achieved excellent agreement, within ∼0.6σ, indicating that potential systematics stemming from source reconstruction algorithms and investigator choices are well under control. We recommend that future studies supersample the PSF as needed and marginalize over multiple algorithms or realizations for the PSF reconstruction to mitigate the systematics associated with the PSF. A future study will measure the time delays of the system WGD 2038−4008 and infer the Hubble constant based on our mass models.

Optimizing EEG Source Reconstruction with Concurrent fMRI-Derived Spatial Priors

Reconstructing EEG sources involves a complex pipeline, with the inverse problem being the most challenging. Multiple inversion algorithms are being continuously developed, aiming to tackle the non-uniqueness of this problem, which has been shown to be partially circumvented by including prior information in the inverse models. Despite a few efforts, there are still current and persistent controversies regarding the inversion algorithm of choice and the optimal set of spatial priors to be included in the inversion models. The use of simultaneous EEG-fMRI data is one approach to tackle this problem. The spatial resolution of fMRI makes fMRI derived spatial priors very convenient for EEG reconstruction, however, only task activation maps and resting-state networks (RSNs) have been explored so far, overlooking the recent, but already accepted, notion that brain networks exhibit dynamic functional connectivity fluctuations. The lack of a systematic comparison between different source reconstruction algorithms, considering potentially more brain-informative priors such as fMRI, motivates the search for better reconstruction models. Using simultaneous EEG-fMRI data, here we compared four different inversion algorithms (minimum norm, MN; low resolution electromagnetic tomography, LORETA; empirical Bayes beamformer, EBB; and multiple sparse priors, MSP) under a Bayesian framework (as implemented in SPM), each with three different sets of priors consisting of: (1) those specific to the algorithm; (2) those specific to the algorithm plus fMRI task activation maps and RSNs; and (3) those specific to the algorithm plus fMRI task activation maps and RSNs and network modules of task-related dFC states estimated from the dFC fluctuations. The quality of the reconstructed EEG sources was quantified in terms of model-based metrics, namely the expectation of the posterior probability P(model|data) and variance explained of the inversion models, and the overlap/proportion of brain regions known to be involved in the visual perception tasks that the participants were submitted to, and RSN templates, with/within EEG source components. Model-based metrics suggested that model parsimony is preferred, with the combination MSP and priors specific to this algorithm exhibiting the best performance. However, optimal overlap/proportion values were found using EBB and priors specific to this algorithm and fMRI task activation maps and RSNs or MSP and considering all the priors (algorithm priors, fMRI task activation maps and RSNs and dFC state modules), respectively, indicating that fMRI spatial priors, including dFC state modules, might contain useful information to recover EEG source components reflecting neuronal activity of interest. Our main results show that providing fMRI spatial derived priors that reflect the dynamics of the brain might be useful to map neuronal activity more accurately from EEG-fMRI. Furthermore, this work paves the way towards a more informative selection of the optimal EEG source reconstruction approach, which may be critical in future studies.

Hippocampal Contribution to Ordinal Psychological Time in the Human Brain.

The chronology of events in time-space is naturally available to the senses, and the spatial and temporal dimensions of events entangle in episodic memory when navigating the real world. The mapping of time-space during navigation in both animals and humans implicates the hippocampal formation. Yet, one arguably unique human trait is the capacity to imagine mental chronologies that have not been experienced but may involve real events-the foundation of causal reasoning. Herein, we asked whether the hippocampal formation is involved in mental navigation in time (and space), which requires internal manipulations of events in time and space from an egocentric perspective. To address this question, we reanalyzed a magnetoencephalography data set collected while participants self-projected in time or in space and ordered historical events as occurring before/after or west/east of the mental self [Gauthier, B., Pestke, K., & van Wassenhove, V. Building the arrow of time… Over time: A sequence of brain activity mapping imagined events in time and space. Cerebral Cortex, 29, 4398-4414, 2019]. Because of the limitations of source reconstruction algorithms in the previous study, the implication of hippocampus proper could not be explored. Here, we used a source reconstruction method accounting explicitly for the hippocampal volume to characterize the involvement of deep structures belonging to the hippocampal formation (bilateral hippocampi [hippocampi proper], entorhinal cortices, and parahippocampal cortex). We found selective involvement of the medial temporal lobes (MTLs) with a notable lateralization of the main effects: Whereas temporal ordinality engaged mostly the left MTL, spatial ordinality engaged mostly the right MTL. We discuss the possibility of a top-down control of activity in the human hippocampal formation during mental time (and space) travels.

NUTMEG: Open Source Software for M/EEG Source Reconstruction.

Neurodynamic Utility Toolbox for Magnetoencephalo- and Electroencephalography (NUTMEG) is an open-source MATLAB-based toolbox for the analysis and reconstruction of magnetoencephalography/electroencephalography data in source space. NUTMEG includes a variety of options for the user in data import, preprocessing, source reconstruction, and functional connectivity. A group analysis toolbox allows the user to run a variety of inferential statistics on their data in an easy-to-use GUI-driven format. Importantly, NUTMEG features an interactive five-dimensional data visualization platform. A key feature of NUTMEG is the availability of a large menu of interference cancelation and source reconstruction algorithms. Each NUTMEG operation acts as a stand-alone MATLAB function, allowing the package to be easily adaptable and scripted for the more advanced user for interoperability with other software toolboxes. Therefore, NUTMEG enables a wide range of users access to a complete “sensor-to- source-statistics” analysis pipeline.

Multispectral bioluminescence tomography-based general iterative shrinkage and threshold algorithm

Bioluminescence tomography (BLT) is a noninvasive optical molecular imaging modality with high sensitivity. The complexity of near-infrared light transmission in biological tissues and the limitation of measurable information place a higher demand on BLT source reconstruction algorithms. In this paper, we present a reconstruction algorithm based on general iterative shrinkage and threshold (GIST), which uses a non-convex smoothly clipped absolute deviation function as the penalty term, and solves a proximal operator problem that has a closed-form solution for the penalty. In addition, we utilize multispectral measurements and an iteratively shrinking permissible region strategy to address the ill-posedness of the BLT inverse problem. To investigate the source location and multi-source resolution abilities of the proposed method, we perform comparisons between three typical sparse reconstruction algorithms based on several groups of simulations and phantom experiments. The reconstruction results demonstrate great advantages of the proposed GIST algorithm in terms of source location accuracy in all considered source settings with different source depths and separations.

Quantifying the Effect of Demixing Approaches on Directed Connectivity Estimated Between Reconstructed EEG Sources.

Electrical activity recorded on the scalp using electroencephalography (EEG) results from the mixing of signals originating from different regions of the brain as well as from artifactual sources. In order to investigate the role of distinct brain areas in a given experiment, the signal recorded on the sensors is typically projected back into the brain (source reconstruction) using algorithms that address the so-called EEG "inverse problem". Once the activity of sources located inside of the brain has been reconstructed, it is often desirable to study the statistical dependencies among them, in particular to quantify directional dynamical interactions between brain areas. Unfortunately, even when performing source reconstruction, the superposition of signals that is due to the propagation of activity from sources to sensors cannot be completely undone, resulting in potentially biased estimates of directional functional connectivity. Here we perform a set of simulations involving interacting sources to quantify source connectivity estimation performance as a function of the location of the sources, their distance to each other, the noise level, the source reconstruction algorithm, and the connectivity estimator. The generated source activity was projected onto the scalp and projected back to the cortical level using two source reconstruction algorithms, linearly constrained minimum variance beamforming and 'Exact' low-resolution tomography (eLORETA). In source space, directed connectivity was estimated using multi-variate Granger causality and time-reversed Granger causality, and compared with the imposed ground truth. Our results demonstrate that all considered factors significantly affect the connectivity estimation performance.

Estimating EEG Source Dipole Orientation Based on Singular-value Decomposition for Connectivity Analysis.

In the last decade, the use of high-density electrode arrays for EEG recordings combined with the improvements of source reconstruction algorithms has allowed the investigation of brain networks dynamics at a sub-second scale. One powerful tool for investigating large-scale functional brain networks with EEG is time-varying effective connectivity applied to source signals obtained from electric source imaging. Due to computational and interpretation limitations, the brain is usually parcelled into a limited number of regions of interests (ROIs) before computing EEG connectivity. One specific need and still open problem is how to represent the time- and frequency-content carried by hundreds of dipoles with diverging orientation in each ROI with one unique representative time-series. The main aim of this paper is to provide a method to compute a signal that explains most of the variability of the data contained in each ROI before computing, for instance, time-varying connectivity. As the representative time-series for a ROI, we propose to use the first singular vector computed by a singular-value decomposition of all dipoles belonging to the same ROI. We applied this method to two real datasets (visual evoked potentials and epileptic spikes) and evaluated the time-course and the frequency content of the obtained signals. For each ROI, both the time-course and the frequency content of the proposed method reflected the expected time-course and the scalp-EEG frequency content, representing most of the variability of the sources (~ 80%) and improving connectivity results in comparison to other procedures used so far. We also confirm these results in a simulated dataset with a known ground truth.

Mapping Brain Activity with Electrocorticography: Resolution Properties and Robustness of Inverse Solutions.

Electrocorticography (ECoG) is an electrophysiological technique that records brain activity directly from the cortical surface with high temporal (ms) and spatial (mm) resolution. Its major limitations are in the high invasiveness and in the restricted field-of-view of the electrode grid, which partially covers the cortex. To infer brain activity at locations different from just below the electrodes, it is necessary to solve the electromagnetic inverse problem. Limitations in the performance of source reconstruction algorithms from ECoG have been, to date, only partially addressed in the literature, and a systematic evaluation is still lacking. The main goal of this study is to provide a quantitative evaluation of resolution properties of widely used inverse methods (eLORETA and MNE) for various ECoG grid sizes, in terms of localization error, spatial dispersion, and overall amplitude. Additionally, this study aims at evaluating how the use of simultaneous electroencephalography (EEG) affects the above properties. For these purposes, we take advantage of a unique dataset in which a monkey underwent a simultaneous recording with a 128 channel ECoG grid and an 18 channel EEG grid. Our results show that, in general conditions, the reconstruction of cortical activity located more than 1cm away from the ECoG grid is not accurate, since the localization error increases linearly with the distance from the electrodes. This problem can be partially overcome by recording simultaneously ECoG and EEG. However, this analysis enlightens the necessity to design inverse algorithms specifically targeted at taking into account the limited field-of-view of the ECoG grid.

A Mathematical Framework for Deep Learning in Elastic Source Imaging

An inverse elastic source problem with sparse measurements is our concern. A generic mathematical framework is proposed which extends a low-dimensional manifold regularization in the conventional source reconstruction algorithms thereby enhancing their performance with sparse data-sets. It is rigorously established that the proposed framework is equivalent to the so-called deep convolutional framelet expansion in machine learning literature for inverse problems. Apposite numerical examples are furnished to substantiate the efficacy of the proposed framework.

Strategies for statistical thresholding of source localization maps in magnetoencephalography and estimating source extent

BackgroundMagnetoencephalography allows defining non-invasively the spatio-temporal activation of brain networks thanks to source localization algorithms. A major difficulty of MNE and beamforming methods, two classically used techniques, is the definition of proper thresholds that allow deciding the extent of activated cortex. New methodWe investigated two strategies for computing a threshold, taking into account the difficult multiple comparison issue. The strategies were based either on parametric statistics (Bonferroni, FDR correction) or on empirical estimates (local FDR and a custom measure based on the survival function). ResultsWe found thanks to the simulations that parametric methods based on the sole estimation of H0 (Bonferroni, FDR) performed poorly, in particular in high SNR situations. This is due to the spatial leakage originating from the source localization methods, which give a ‘blurred’ reconstruction of the patch extension: the higher the SNR, the more this effect is visible. Comparison with existing methodsAdaptive methods such as local FDR or our proposed ‘concavity threshold’ performed better than Bonferroni or classical FDR. We present an application to real data originating from auditory stimulation in MEG. ConclusionIn order to estimate source extent, adaptive strategies should be preferred to parametric statistics when dealing with ‘leaking’ source reconstruction algorithms.

Modeling of Large-Scale Functional Brain Networks Based on Structural Connectivity from DTI: Comparison with EEG Derived Phase Coupling Networks and Evaluation of Alternative Methods along the Modeling Path.

In this study, we investigate if phase-locking of fast oscillatory activity relies on the anatomical skeleton and if simple computational models informed by structural connectivity can help further to explain missing links in the structure-function relationship. We use diffusion tensor imaging data and alpha band-limited EEG signal recorded in a group of healthy individuals. Our results show that about 23.4% of the variance in empirical networks of resting-state functional connectivity is explained by the underlying white matter architecture. Simulating functional connectivity using a simple computational model based on the structural connectivity can increase the match to 45.4%. In a second step, we use our modeling framework to explore several technical alternatives along the modeling path. First, we find that an augmentation of homotopic connections in the structural connectivity matrix improves the link to functional connectivity while a correction for fiber distance slightly decreases the performance of the model. Second, a more complex computational model based on Kuramoto oscillators leads to a slight improvement of the model fit. Third, we show that the comparison of modeled and empirical functional connectivity at source level is much more specific for the underlying structural connectivity. However, different source reconstruction algorithms gave comparable results. Of note, as the fourth finding, the model fit was much better if zero-phase lag components were preserved in the empirical functional connectome, indicating a considerable amount of functionally relevant synchrony taking place with near zero or zero-phase lag. The combination of the best performing alternatives at each stage in the pipeline results in a model that explains 54.4% of the variance in the empirical EEG functional connectivity. Our study shows that large-scale brain circuits of fast neural network synchrony strongly rely upon the structural connectome and simple computational models of neural activity can explain missing links in the structure-function relationship.

Multi-Dimensional Dynamics of Human Electromagnetic Brain Activity.

Magnetoencephalography (MEG) and electroencephalography (EEG) are invaluable neuroscientific tools for unveiling human neural dynamics in three dimensions (space, time, and frequency), which are associated with a wide variety of perceptions, cognition, and actions. MEG/EEG also provides different categories of neuronal indices including activity magnitude, connectivity, and network properties along the three dimensions. In the last 20 years, interest has increased in inter-regional connectivity and complex network properties assessed by various sophisticated scientific analyses. We herein review the definition, computation, short history, and pros and cons of connectivity and complex network (graph-theory) analyses applied to MEG/EEG signals. We briefly describe recent developments in source reconstruction algorithms essential for source-space connectivity and network analyses. Furthermore, we discuss a relatively novel approach used in MEG/EEG studies to examine the complex dynamics represented by human brain activity. The correct and effective use of these neuronal metrics provides a new insight into the multi-dimensional dynamics of the neural representations of various functions in the complex human brain.

Statistical and systematic uncertainties in pixel-based source reconstruction algorithms for gravitational lensing

Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularisation, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the lens mapping but is irregular, and an adaptive Cartesian grid. We also consider regularisation schemes that minimise derivatives of the source (using two finite difference methods) and introduce a scheme that minimises deviations from an analytic source profile. Careful choice of gridding and regularisation can reduce "discreteness noise" in the $\chi^2$ surface that is inherent in the pixel-based methodology. With a gridded source, some degree of interpolation is unavoidable, and errors due to interpolation need to be taken into account (especially for high signal-to-noise data). Different realisations of the noise and telescope pointing lead to slightly different values for lens model parameters, and the scatter between different "observations" can be comparable to or larger than the model uncertainties themselves. The same effects create scatter in the lensing magnification at the level of a few percent for a peak signal-to-noise ratio of 10, which decreases as the data quality improves.

On a various noise source reconstruction algorithms in VVER-1000 reactor core

In present study, the neutron noise source is reconstructed using three different unfolding techniques in a typical VVER-1000 reactor core. In first stage, the neutron noise calculation based on Galerkin finite element method (GFEM) is performed; in which the neutron noise in two energy group due to the noise sources of type absorber of variable strength and vibrating absorber is calculated. The neutron noise due to inadvertent loading of a fuel assembly in an improper position (ILFAIP), as a new defined noise source in the neutron noise studies, is calculated as well. In the second stage, the inversion, zoning and scanning methods are applied for reconstruction of the noise source of type absorber of variable strength. Also, improved scanning method (ISM) is used to reconstruct the noise source of type vibrating absorber. To solve the system of equations in the inversion method, four different algorithms are used. The obtained results from various unfolding methods are then compared. Finally, a sensitivity analysis of mentioned methods to different parameters like the location of noise source in the reactor core, number of available detectors and fuel burn up is performed.

Simulation chain for acoustic ultra-high energy neutrino detectors

Acoustic neutrino detection is a promising approach for large-scale ultra-high energy neutrino detectors in water. In this paper, a Monte Carlo simulation chain for acoustic neutrino detection devices in water is presented. It is designed within the SeaTray/IceTray software framework. Its modular architecture is highly flexible and makes it easy to adapt to different environmental conditions, detector geometries, and hardware. The simulation chain covers the generation of the acoustic pulse produced by a neutrino interaction and the propagation to the sensors within the detector. In this phase of the development, ambient and transient noise models for the Mediterranean Sea and simulations of the data acquisition hardware, similar to the one used in ANTARES/AMADEUS, are implemented. A pre-selection scheme for neutrino-like signals based on matched filtering is employed, as it can be used for on-line filtering. To simulate the whole processing chain for experimental data, signal classification and acoustic source reconstruction algorithms are integrated. In this contribution, an overview of the design and capabilities of the simulation chain will be given, and some applications and preliminary studies will be presented.

Recent Developments in Breast Tomosynthesis Imaging

This review gives an overview of current methods in digital breast tomosynthesis (DBT) and how they have developed from tomography applications elsewhere. Particular attention is given to patents which have impacted on currently available technology or offer a glimpse at future developments. A number of different approaches to clinical breast tomosynthesis systems are examined including different geometries, x-ray source assemblies, detector configurations, reconstruction algorithms and image display and analysis methods. Current studies in the clinical efficacy of DBT are also discussed. Keywords: ART – Arithmetic Reconstruction Technique, breast dosimetry, breast imaging, breast screening trial, CAD – computer aided detection, DBT – digital breast tomosynthesis, FBP – filtered back projection, FFDM - Full field digital mammography, reconstruction algorithm, tomosynthesis.

TH-D-342-04: Advanced CT Image Reconstruction Algorithms Via Compressed Sensing

The key components of an x-ray computed tomography system are the source, detector, and image reconstruction algorithms. The introduction of multi-row detectors has enabled larger scanning coverage, higher spatial and faster complete organ scanning in the general purpose CT scanners. These improvements have enabled a variety of advanced clinical applications. The introduction of flat-panel detectors has enabled dedicated cone-beam CT in breast imaging, image-guided interventions, and image-guided radiation therapy. There is a constant interplay between the development of new and improved CT systems and advanced CT image reconstruction algorithms. New CT systems require advanced image reconstruction algorithms, and breakthroughs in image reconstruction algorithms may also enable future innovations in the future design of CT systems. The Shannon sampling theory is the foundation of conventional linear image reconstruction algorithms such as the Fourier transform and filtered backprojection methods. In these conventional image reconstruction frameworks, the violation of the Shannon sampling criterion often results in aliasing artifacts such as streaks in the reconstructed images. Recently, a new sampling theory, i.e., compressive sampling, has been formulated. It has been proven that accurate image reconstruction is possible using highly undersampled data sets provided that a nonlinear iterative image reconstruction method is utilized. This nonlinear iterative image reconstruction method is widely referred to as compressed sensing (CS). Based on the CS theory, some other generalized CS image reconstruction algorithms such as prior image constrained compressed sensing (PICCS) were recently proposed to reconstruct CT images. In this talk, we will discuss the potential impact of CS-based CT image reconstruction algorithms and their impact on current and future CT development. Educational Objectives: 1. Understand violation of sampling criterion may cause streaking artifacts in conventional linear image reconstruction algorithm. 2. Understand Compressed Sensing based image reconstruction algorithms can generate streak-free image using a highly undersampled data set. 3. Understand the potential benefit of PICCS algorithm in radiation dose reduction and improve temporal resolution using a slow gantry.

Consistency conditions upon 3D CT data and the wave equation

Source trajectories and reconstruction algorithms for clinical volumetric computerized tomography (VCT) will require optimization for efficiency and image quality. VCT data is highly overdetermined, satisfying an ultrahyperbolic partial differential equation. Characteristic boundary value problems for the hyperbolic wave equation and ultrahyperbolic equation are compared, focusing in this paper on a mathematically instructive open-gantry VCT geometry. This example provides physical insight into consistency conditions upon VCT data, clearly showing which information about the object can and cannot be recovered from a set of measured projections. Furthermore, this example demonstrates that efficient numerical solvers for the ultrahyperbolic equation can provide tremendous flexibility in the choice of reconstruction algorithm.

Source analysis of lesional frontal-lobe epilepsy.

Patients with frontal-lobe epilepsy comprise the second largest group undergoing epilepsy surgery. It has been reported that the difficulty in localizing the epileptogenic zone in these patients is due to the rapid spread of the epileptiform activity within the frontal lobe and to adjoining regions of the brain. We formulated the question of whether the functional localization of dynamic sources of interictal activity in patients with well-defined frontal lesions would yield clear evidence regarding both the topology of the primary sources in relation to the epileptogenic lesion and the pattern of spread of the epileptiform activity throughout the brain. In order to achieve this, we used high-resolution EEG recordings combined with MRI, and advanced source-reconstruction algorithms. In this article, the source-imaging procedures used will be discussed extensively, based on one exemplary patient with complex partial FLE.